“London’s supposed to be this melting pot, but that’s bullshit, innit.” A guy is talking to a woman he’s trying to pull in London Unplugged – a collection of 10 shorts by emerging film-makers, all with London as their backdrop. This is an earnest, uneven project – an anthology of struggle in the city – that at its best shows diverse London as it’s rarely seen in the movies, shot in crappy flats with stories about the migrant experience, loneliness and being broke. What struck me watching it was the uncomfortable truth in that “melting pot” comment – Londoners pride themselves on openness but plenty are guilty of barely tiptoeing outside their own postcodes and friendship networks.

Only a few of the shorts are successful. In Unchosen, a young Iranian woman is told she has no grounds to appeal her rejected asylum claim. Her lawyer correctly suspects she’s hiding something – a secret that carries a death sentence in Iran. The storyline thoughtfully reverses the stereotype of “bogus” asylum-seekers. In my favourite, a rosy-cheeked toddler cheerfully takes herself off for a solo day trip to Tate Modern after her mum is distracted by a work email. This piece has no social message and is entirely unrealistic – and including a happy ending that doesn’t involve A&E or social services – but it tickled me.

Inevitably, a good chunk of the shorts are underdeveloped or let down by amateur acting. But it is an impressive achievement on a next-to-nothing budget. And how refreshing to see London without its makeup on. This is a film devoid of Richard Curtis-like fairytale – with the exception of one scene in which a woman gazes out of her window at the stars. Stars! The only place my two-year-old has seen stars in London is in books.